Seminars and Colloquia by Series

Friday, October 9, 2009 - 15:00 , Location: Skiles 269 , Igor Belegradek , Georgia Tech , Organizer:
This 2 hour talk is a gentle introduction to simply-connected sugery theory (following classical work by Browder, Novikov, and Wall). The emphasis will be on classification of high-dimensional manifolds and understanding concrete examples.
Friday, October 2, 2009 - 15:00 , Location: Skiles 269 , Igor Belegradek , Georgia Tech , Organizer:
This 2 hour talk is a gentle introduction to simply-connected sugery theory (following classical work by Browder, Novikov, and Wall). The emphasis will be on classification of high-dimensional manifolds and understanding concrete examples.
Friday, September 25, 2009 - 15:00 , Location: Skiles 269 , Anh Tran , Georgia Tech , Organizer:

(This is a 2 hour lecture.)

In this talk I will give a quick review of classical invariants of Legendrian knots in a 3-dimensional contact manifold (the topological knot type, the Thurston-Bennequin invariant and the rotation number). These classical invariants do not completely determine the Legendrian isotopy type of Legendrian knots, therefore we will consider Contact homology (aka Chekanov-Eliashberg DGA), a new invariant that has been defined in recent years. We also discuss the linearization of Contact homology, a method to extract a more computable invariant out of the DGA associated to a Legendrian knot.
Friday, September 18, 2009 - 14:00 , Location: Skiles 269 , John Etnyre , Georgia Tech , Organizer:
We will discuss how to put a hyperbolic structure on various surface and 3-manifolds. We will being by discussing isometries  of hyperbolic space in dimension 2 and 3. Using our understanding of these isometries we will explicitly construct hyperbolic structures on all close surfaces of genus greater than one and a complete finite volume hyperbolic structure on the punctured torus. We will then consider the three dimensional case where we will concentrate on putting hyperbolic structures on knot complements. (Note: this is a 1.5 hr lecture)
Friday, September 11, 2009 - 15:00 , Location: Skiles 269 , John Etnyre , Georgia Tech , Organizer:
We will discuss how to put a hyperbolic structure on various surface and 3-manifolds. We will being by discussing isometries  of hyperbolic space in dimension 2 and 3. Using our understanding of these isometries we will explicitly construct hyperbolic structures on all close surfaces of genus greater than one and a complete finite volume hyperbolic structure on the punctured torus. We will then consider the three dimensional case where we will concentrate on putting hyperbolic structures on knot complements. (Note: this is a 2 hr seminar)
Friday, April 24, 2009 - 15:00 , Location: Skiles 269 , Thang Le , School of Mathematics, Georgia Tech , Organizer: John Etnyre

These are two hour lectures.

We will develop general theory of quantum invariants based on sl_2 (the simplest Lie algebra): The Jones polynomials, the colored Jones polynomials, quantum sl_2 groups, operator invariants of tangles, and relations with the Alexander polynomial and the A-polynomials. Optional: Finite type invariants and the Kontsevich integral.
Friday, April 17, 2009 - 15:00 , Location: Skiles 269 , Thang Le , School of Mathematics, Georgia Tech , Organizer: John Etnyre

These are two hour lectures.

We will develop general theory of quantum invariants based on sl_2 (the simplest Lie algebra): The Jones polynomials, the colored Jones polynomials, quantum sl_2 groups, operator invariants of tangles, and relations with the Alexander polynomial and the A-polynomials. Optional: Finite type invariants and the Kontsevich integral.
Friday, April 10, 2009 - 15:00 , Location: Skiles 269 , Thang Le , School of Mathematics, Georgia Tech , Organizer: John Etnyre

These are two hour talks.

We will develop general theory of quantum invariants based on sl_2 (the simplest Lie algebra): The Jones polynomials, the colored Jones polynomials, quantum sl_2 groups, operator invariants of tangles, and relations with the Alexander polynomial and the A-polynomials. Optional: Finite type invariants and the Kontsevich integral.
Friday, February 27, 2009 - 15:05 , Location: Skiles 269 , Igor Belegradek , Ga Tech , Organizer: John Etnyre
Comparison geometry studies Riemannian manifolds with a given curvature bound. This minicourse is an introduction to volume comparison (as developed by Bishop and Gromov), which is fundamental in understanding manifolds with a lower bound on Ricci curvature. Prerequisites are very modest: we only need basics of Riemannian geometry, and fluency with fundamental groups and metric spaces. In the third (2 hour) lecture I shall prove volume and Laplacian comparison theorems.
Friday, February 20, 2009 - 15:00 , Location: Skiles 269 , Igor Belegradek , Ga Tech , Organizer: John Etnyre
 Comparison geometry studies Riemannian manifolds with a given curvature bound. This minicourse is an introduction to volume comparison (as developed by Bishop and Gromov), which is fundamental in understanding manifolds with a lower bound on Ricci curvature. Prerequisites are very modest: we only need basics of Riemannian geometry, and fluency with fundamental groups and metric spaces. The second (2 hour) lecture is about Gromov-Hausdorff convergence, which provides a natural framework to studying degenerations of Riemannian metrics. 

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